1. Field of the Invention
The present invention is directed to a method and system for fairing meshes. More specifically, the present invention relates to diffusing curvature in meshes or clouds of vertices.
2. Description of the Related Art
In the field of computer graphics, surface fairing is performed to improve the shape of a mesh. Fairing has been described as the process of smoothing a mesh or surface, often by minimizing a fairness function. In some cases, meshes have holes or gaps, which may be the result of inadequate sampling, a user deleting part of a mesh, etc. Fairing is useful for constructing mesh patches that give a fair interpolation of the shape of the adjoining mesh. Further background information may be found in “Filling Holes in Meshes”, Proceedings of the Eurographics/ACM SIGGRAPH symposium on Geometry processing, p. 200-205, June 2003”, by Peter Liepa; “Geometric Fairing of Irregular Meshes for Free-Form Surface Design”, Computer-Aided Geometric Design, 18(4):359-379, May 2001, by Schneider and Kobbelt; and “Implicit Fairing of Irregular Meshes Using Diffusion and Curvature Flow”, SIGGRAPH 99 Conference Proceedings, pages 317-324, by Desbrun, Meyer, Schröder, and Barr.
There is a need for an efficient fairing process that produces reasonable diffusions or distributions of boundary curvature into a mesh that is being faired.